Civil Engineering Reference
In-Depth Information
The squared-velocity-pondered length of the circle C in Figure 5.C.1 is
2
π
υ
2
(θ)R
d
θ
=
4
πυ
o
R
(5.C.5)
0
If the porosity is close to 1,
is given by
2
υ
o
4
πυ
o
RL
=
1
2
πLR
=
(5.C.6)
where
L
is the total length of the cylinder per unit volume of fibrous material.
The perturbation in the velocity field created by one fibre decreases as
R
2
/D
2
,where
D
is the distance from the axis of the fibre. The order of magnitude of the distance
between the closest fibres is 10 times, or more, as large as
R
for the usual glass wools
and rock wools, and the interaction between the different fibres can be neglected.
The radius
R
expressed in metres can be obtained from the empirical expression in
Bies an Hansen (1980)
σR
2
ρ
−
1
.
53
1
=
0
.
79
×
10
−
9
(5.C.7)
where
σ
is the flow resistivity expressed in N m
−
4
sand
ρ
1
the density expressed in
kg/m
3
.
References
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